A repeater can be a large transmission station. An extender can be an added antenna or a power booster. I don't recommend a repeater, it's kind of like having your own radio station.
I have heard (unofficially) roughly a 20-mile radius. My office is right around 20 miles from the repeater in my city and I get nearly-perfect reception solely from the repeater. I have Sirius, by the way. I don't know much about XM's repeaters, but ...
Yes you just put the repeater between the router and the destination, im not sure about wireless routers being repeaters, i dont think they can be though, id stick to the repeater to be safe.